The present disclosure relates to gaming machines and networks and, more particularly, to games of chance involving player input and selection, such as a Wheel of Fortune® game.
Gaming in the United States is divided into Class I, Class II and Class III games. Class I gaming includes social games played for minimal prizes, or traditional ceremonial games. Class II gaming includes bingo games, pull tab games if played in the same location as bingo games, lotto, punch boards, tip jars, instant bingo, and other games similar to bingo. Class II games can be implemented in a Central Determination configuration, in which a central computer or system determines game outcomes regardless of any player input or decisions. Class III gaming includes any game that is not a Class I or Class II game, such as a game of chance typically offered in non-Indian, state-regulated casinos. Many games of chance that are played on gaming machines fall into the Class II and Class III categories of games.
One trend in the design of Class III games is the reliance upon player input for determining the outcome of a game, when several outcomes are possible. Games that involve player choice are generally more interesting for game players because of the increased enjoyment of participation in the game. For example, in a Wheel of Fortune® game, as shown in FIG. 1, the player is presented with a wheel 100 with outcomes disposed about the center of the wheel in a pie configuration, as shown. In this example, the player sees 12 possible outcomes or award amounts. The particular amount awarded to the player depends on which outcome the pointer 105 points to when the wheel stops after it is spun. In the example of FIG. 1, the wheel 100 has been spun and stopped with the pointer 105 pointing to a $30 amount. Thus, the player is awarded $30 from this spin.
In FIG. 2, the wheel 100 is shown from the perspective of a gaming machine on which the Wheel of Fortune® game is played. In FIG. 2, the gaming machine manages the particular outcomes or award amounts of FIG. 1 as a number of stops corresponding to the number of award amounts. For instance, in this example, stop 10 is associated with the $150 amount, stop 9 is associated with the $50 amount, stop 8 is associated with the $15 amount, stop 7 is associated with the $75 amount, and so forth. Thus, when the wheel stops with the pointer 105 pointing at the $30 award amount, the gaming machine has selected the associated stop 0 as the outcome, providing that award amount.
In generating outcomes for a game of chance, a pay table is often used. The pay table contains the award amounts, or “payouts” associated with each stop. In addition, the pay table includes a set of fixed probabilities associated with each stop and associated award amount. In this way, the outcome on any given spin or play is randomly determined according to the fixed probabilities defined in the pay table. For example, in Table 1 below, the stops and associated payouts or award amounts of FIGS. 1 and 2 are shown with associated weights in the far-right column. Thus, stop 1, with a weight of 14, is generally the most likely outcome. Those skilled in the art will appreciate that the weights in the far-right column of Table 1 can be divided by the sum of all the weights for Table 1 to show the corresponding probability for each weight.
TABLE 1StopPayoutWeight03091201426583251045002550116401077598151095010101502112510
In some implementations, the weights, as shown in Table 1, define a range of Random Number Generator (RNG) values that will determine the stop. For example, in Table 2, the weight associated with stop 0 is 9, so this weight is assigned a range of nine numbers, 0-8. Similarly, the weight associated with stop 1 is 14, so this stop is assigned the next thirteen numbers, 9-22. The range of numbers associated with each of the remaining stops is similarly calculated, as shown in Table 2.
TABLE 2StopPayoutWeightRange03090-812014 9-22265823-303251031-404500241-425501143-536401054-63775964-728151073-829501083-9210150293-94112510 95-104
When the gaming machine randomly determines one of the stops, using the pay table shown in Table 2, the gaming machine will generate a number from 0 to 104. Then, the stop having the range in which the generated number falls is the stop determined for the outcome of the game, or spin in the Wheel of Fortune® example. For instance, using Table 2, when the random number 38 is generated, stop 3 is selected.
Payout weights and an average payout for the pay table can be calculated. This average payout is the average award a player can expect to receive for a game play session, e.g., spin. Table 3 below incorporates the same “stop,” “payout,” and “weight” entries of Tables 1 and 2. In addition, a fourth column in Table 3 below shows the payout weight associated with each stop in the pay table. This payout weight is calculated by multiplying the payout of the particular stop with the weight associated with that stop. Thus, the payout weight for stop 0 is 9·30=270. Similarly, the payout weight for stop 2 is 8·65=520.
TABLE 3StopPayoutWeightPayout * Weight030927012014280265852032510250450021000550115506401040077596758151015095010500101502300112510250Total1055145Average49
In Table 3, when all of the payout weights are calculated for the stops in the pay table, the total payout weight can be divided by the sum of all of the weights to determine the average payout, i.e. 5145/105=49. Thus, in a game applying the pay structure of Table 3, the player can expect an average payout of $49.
As mentioned above, a trend in modern gaming is to allow a player to make a selection to influence the outcome of a game. In one implementation of this trend, Wheel of Fortune® games have been designed to allow a player to select one of a plurality of pointers when spinning the wheel. Thus, the award amount will depend on which pointer the player selected. For example, FIG. 3 shows wheel 100 of FIGS. 1 and 2. In addition to pointer 105, the implementation of FIG. 3 includes pointers 305 and 310. These pointers are situated as desired about the wheel, as shown in FIG. 3. In one example, as shown in FIG. 4, the pointers have respective colors. For example, pointer 105 is red, pointer 305 is blue, and pointer 310 is yellow. Before the player spins the wheel, the player chooses which pointer, red, blue or yellow, to play. After the wheel is spun, the player is given the award indicated by the pointer chosen.
While FIG. 3 shows the addition of pointers 305 and 310 to wheel 100, the functionality of the gaming machine in determining an outcome is essentially the same as that described above with respect to FIGS. 1 and 2 and Tables 1-3. That is, the gaming machine manages the wheel as a collection of stops. In FIG. 4, the view of the wheel from the perspective of the gaming machine is shown. As one can see, the stops are the same as the stops set forth in FIG. 2. The only difference is the inclusion of the additional pointers. However, these pointers do not have any impact on the operation of the gaming machine in generating outcomes or stops. The gaming machine determines a stop or outcome for red pointer 105, as in FIGS. 1 and 2 above.
Thus, in the example of FIGS. 3 and 4, after the wheel is spun, applying the pay tables of Tables 1-3, the gaming machine determines that stop 0, or the award of $30, will be the outcome. Thus, the wheel stops with pointer 105 pointing at stop 0 or $30, as in FIGS. 1 and 2. However, the additional variable in FIGS. 3 and 4 is the opportunity of the player to select the blue pointer 305 or yellow pointer 310. As shown in FIG. 4, when the wheel stops at stop 0, the red pointer points at stop 0. The blue pointer, however, points at stop 2, and the yellow pointer points at stop 6. Thus, even though the gaming machine operates in the same manner as described above, the final outcome or payout awarded is dependent on the player's selected pointer. In the example shown in FIGS. 3 and 4, if the player had selected the blue pointer, a $65 payout would have been awarded. If the player had selected the yellow pointer, a $40 payout would have been awarded. Accordingly, the dependence upon player choice in FIGS. 3 and 4 affects the average payout, unlike the single pointer scenario described above with reference to FIGS. 1 and 2.
Table 4 shows the payouts associated with the respective pointers of FIGS. 3 and 4.
TABLE 4PayoutPayoutPayoutWeightMachineWeightWeightYellowatSelectedRed Pointerat RedBlue Pointerat BluePointerYellowStopWeightPayoutPointerPayoutPointerPayoutPointer09302706558540360114202802535075105028655205004000151203102525050500505004250010004080150300511505507582525275610404001515030300797567550450201808101515015015006565091050500252502525010 21503003060500100011 10252502020050500Totals105514589505485Averages4985.238152.2381
In the table above, one can see that when the gaming machine generates a stop of 0, then the red pointer would award the player $30, but the blue pointer would award the player $65. The probability of the $30 payout landing on position 0 is the same as the probability of the $65 payout landing on the blue pointer. However, the probability of the $30 payout landing on the red pointer is not the same as the probability of the $30 payout landing on the blue pointer. Thus, it should be clear from Table 4 that the probability of a certain outcome or payout amount at the red pointer is not the same as the probability that the same amount will be output at the blue pointer or yellow pointer. Each pointer has a different set of probabilities or weights assigned to its outcomes or payout amounts.
In Table 4 above, average payouts can be calculated for the respective pointers, applying the same computations described above with respect to Table 3. Thus, when the player selects the red pointer, he can expect an average payout of $49, the same as Table 3. If, however, the player selects the blue pointer, he can expect to receive an average payout of $85.2381. If the player selects the yellow pointer, he can expect an average payout of $52.2381.
As shown in Table 4 above, the blue pointer has a higher average payout than the other pointers. When the player learns the pointer with the highest average yield, either from discovering the pay table or gathering general knowledge from experience, the player will always choose the pointer having the highest average yield. Thus, in Table 4 above, if the player were aware of the average payouts of the respective pointers, the player would always pick the blue pointer. Such discovery is inevitable in the gaming world. When this discovery is made, the entertainment associated with the fundamental game play feature of pointer selection is removed. The entertainment value of the entire game is significantly reduced, and the game can become unexciting.
It is therefore desirable to implement a game of chance involving player choice in a Central Determination, Class II/Bingo gaming system, and a Class III configuration to provide the enjoyment associated with increased participation in the game, but compensate for the player choice to produce the same average payout regardless of the player selection.